Matt, my experience of my mother's dementia was not 24x7. For much of the time, she knew who we were, what was going on, and could hold a normal conversation. Much of that was due to the familiarity of her surroundings. Walking the same way to Mass every day. It was only in the last couple of years of her life that she really struggled with her memory. When she was in the nursing home, she sometimes was aware that she knew us, but didn't know exactly who we were. For instance, she would often ask about my children and to be honest, I would use that as an excuse to leave - I have to get home to make the kids' dinner.
Trying to take on an older woman with dementia and 2 kids at the same time, sound like a recipe for disaster. I think you have the best of intentions, but you need to be realistic. It's peoples' lives we're talking about. I don't have a disability, and would struggle to to take care of either the mother or the kids, but I certainly couldn't do both.
Btw, how do you feel about inviting kkjason to join us for dinner on 15th?